Syria maintains that it engaged the aircraft in its airspace "according to the laws that govern such situations".
The Turkish and Syrian navies are still searching for the two crew members.
Ankara has promised its response will be strong, decisive and legitimate once it has ascertained all the circumstances surrounding the incident.
In an interview with TRT television on Sunday, Mr Davutoglu asserted that the unarmed F-4 Phantom had entered Syrian airspace by mistake on Friday but had left by the time it was shot down several minutes later.
"According to our conclusions, our plane was shot down in international airspace, 13 nautical miles (24km) from Syria," he said.
According to international law, a country's airspace extends 12 nautical miles (22.2km) from its coastline, corresponding with its territorial waters.